This document proposes a multilayer network representation and simulated annealing optimization approach for assembly line balancing problems. Key points:
- A multilayer network model is presented to represent the skills, tools, precedence constraints, and assignments of tasks to operators in an assembly line.
- A multi-objective function is defined that considers minimizing cycle time, training costs, and equipment costs. Analytic hierarchy process is used to determine the weights of each objective.
- A simulated annealing algorithm is developed that uses a sequential representation of the task assignments and neighborhood search to optimize the multi-objective function while satisfying precedence constraints.
- The method is demonstrated on a case study of a wire harness manufacturing process, showing the efficiency of the
This document discusses adaptive system-level scheduling under fluid traffic flow conditions in multiprocessor systems. It proposes a scheduling mechanism that accounts for traffic-centric system design. The mechanism evaluates scheduling methods based on effectiveness, robustness, and flexibility. It also introduces a processor-FPGA scheduling approach that reduces schedule length by taking advantage of FPGA reconfiguration. Simulation results show that processor-FPGA scheduling outperforms multiprocessor-only scheduling under certain traffic conditions. Future work will focus on formulating a traffic-centric scheduling method.
SCIENTIFIC WORKFLOW CLUSTERING BASED ON MOTIF DISCOVERYijcseit
This document summarizes a research paper that proposes a method for clustering scientific workflows based on motif discovery. The method first extracts workflow motifs, which are common sub-patterns within workflows. It then represents workflows as sets of embedded motifs using a deep neural network. Finally, it applies a k-means clustering algorithm using a selection method based on the Shuffled Frog Leaping Algorithm to identify the optimal number of clusters. The method is tested on a dataset of 120 scientific workflows and is found to perform better than alternative algorithms like particle swarm optimization and genetic algorithms for selecting the number of clusters.
SCIENTIFIC WORKFLOW CLUSTERING BASED ON MOTIF DISCOVERYijcseit
This document summarizes a research paper that proposes a method for clustering scientific workflows based on motif discovery. It first represents workflows as sets of tasks and encodes tasks as recurring steps using a deep neural network. It then quantifies workflow motifs by identifying common sub-workflow structures. Finally, it clusters the workflows using a set-based k-means clustering approach and a shuffled frog leaping algorithm to select the optimal number of clusters k. The method was tested on a dataset of 120 scientific workflows and showed improved performance over particle swarm optimization and genetic algorithms for selecting k.
IRJET- Advance Approach for Load Balancing in Cloud Computing using (HMSO) Hy...IRJET Journal
This document proposes a new hybrid multi-swarm optimization (HMSO) algorithm for load balancing in cloud computing. It aims to minimize response time and costs while improving resource utilization and customer satisfaction. The HMSO algorithm uses multi-level particle swarm optimization to find an optimal resource allocation solution. Simulation results show that the proposed HMSO technique reduces response time and datacenter costs compared to other algorithms. It also achieves a more balanced load distribution across resources.
International Refereed Journal of Engineering and Science (IRJES) is a peer reviewed online journal for professionals and researchers in the field of computer science. The main aim is to resolve emerging and outstanding problems revealed by recent social and technological change. IJRES provides the platform for the researchers to present and evaluate their work from both theoretical and technical aspects and to share their views.
www.irjes.com
This document proposes a genetic algorithm called Workflow Scheduling for Public Cloud Using Genetic Algorithm (WSGA) to optimize the cost of executing workflows in the public cloud. It discusses how genetic algorithms can be applied to the workflow scheduling problem to generate optimal schedules. The WSGA represents potential scheduling solutions as chromosomes, uses a fitness function to evaluate scheduling costs, and applies genetic operators like selection, crossover and mutation to evolve new schedules over multiple iterations. The goal is to minimize total execution cost while meeting workflow dependencies and deadline constraints. An experimental setup is described and the WSGA approach is claimed to reduce costs more than other heuristic scheduling algorithms for communication-intensive workflows.
LoadAwareDistributor: An Algorithmic Approach for Cloud Resource AllocationIRJET Journal
This document summarizes research on load balancing algorithms for cloud resource allocation. It proposes a new LoadAwareDistributor algorithm that prioritizes virtual machines with lower CPU utilization to improve efficiency. A literature review covers existing load balancing techniques and their goals. The proposed algorithm is evaluated through simulation and shown to improve metrics like VM utilization and task completion time over round-robin methods. The study advocates for future algorithm advances incorporating machine learning to better address dynamic load balancing challenges in cloud computing environments.
This document describes a multi-path routing algorithm for IP networks based on flow optimization. It presents an intra-domain routing algorithm that uses multi-commodity flow optimization to enable load-sensitive forwarding over multiple paths without being constrained by traditional routing protocols like OSPF. The key idea is to aggregate all traffic destined for the same egress node into one commodity during optimization, reducing the number of commodities significantly. This makes the computation tractable and allows forwarding based on destination addresses.
This document discusses adaptive system-level scheduling under fluid traffic flow conditions in multiprocessor systems. It proposes a scheduling mechanism that accounts for traffic-centric system design. The mechanism evaluates scheduling methods based on effectiveness, robustness, and flexibility. It also introduces a processor-FPGA scheduling approach that reduces schedule length by taking advantage of FPGA reconfiguration. Simulation results show that processor-FPGA scheduling outperforms multiprocessor-only scheduling under certain traffic conditions. Future work will focus on formulating a traffic-centric scheduling method.
SCIENTIFIC WORKFLOW CLUSTERING BASED ON MOTIF DISCOVERYijcseit
This document summarizes a research paper that proposes a method for clustering scientific workflows based on motif discovery. The method first extracts workflow motifs, which are common sub-patterns within workflows. It then represents workflows as sets of embedded motifs using a deep neural network. Finally, it applies a k-means clustering algorithm using a selection method based on the Shuffled Frog Leaping Algorithm to identify the optimal number of clusters. The method is tested on a dataset of 120 scientific workflows and is found to perform better than alternative algorithms like particle swarm optimization and genetic algorithms for selecting the number of clusters.
SCIENTIFIC WORKFLOW CLUSTERING BASED ON MOTIF DISCOVERYijcseit
This document summarizes a research paper that proposes a method for clustering scientific workflows based on motif discovery. It first represents workflows as sets of tasks and encodes tasks as recurring steps using a deep neural network. It then quantifies workflow motifs by identifying common sub-workflow structures. Finally, it clusters the workflows using a set-based k-means clustering approach and a shuffled frog leaping algorithm to select the optimal number of clusters k. The method was tested on a dataset of 120 scientific workflows and showed improved performance over particle swarm optimization and genetic algorithms for selecting k.
IRJET- Advance Approach for Load Balancing in Cloud Computing using (HMSO) Hy...IRJET Journal
This document proposes a new hybrid multi-swarm optimization (HMSO) algorithm for load balancing in cloud computing. It aims to minimize response time and costs while improving resource utilization and customer satisfaction. The HMSO algorithm uses multi-level particle swarm optimization to find an optimal resource allocation solution. Simulation results show that the proposed HMSO technique reduces response time and datacenter costs compared to other algorithms. It also achieves a more balanced load distribution across resources.
International Refereed Journal of Engineering and Science (IRJES) is a peer reviewed online journal for professionals and researchers in the field of computer science. The main aim is to resolve emerging and outstanding problems revealed by recent social and technological change. IJRES provides the platform for the researchers to present and evaluate their work from both theoretical and technical aspects and to share their views.
www.irjes.com
This document proposes a genetic algorithm called Workflow Scheduling for Public Cloud Using Genetic Algorithm (WSGA) to optimize the cost of executing workflows in the public cloud. It discusses how genetic algorithms can be applied to the workflow scheduling problem to generate optimal schedules. The WSGA represents potential scheduling solutions as chromosomes, uses a fitness function to evaluate scheduling costs, and applies genetic operators like selection, crossover and mutation to evolve new schedules over multiple iterations. The goal is to minimize total execution cost while meeting workflow dependencies and deadline constraints. An experimental setup is described and the WSGA approach is claimed to reduce costs more than other heuristic scheduling algorithms for communication-intensive workflows.
LoadAwareDistributor: An Algorithmic Approach for Cloud Resource AllocationIRJET Journal
This document summarizes research on load balancing algorithms for cloud resource allocation. It proposes a new LoadAwareDistributor algorithm that prioritizes virtual machines with lower CPU utilization to improve efficiency. A literature review covers existing load balancing techniques and their goals. The proposed algorithm is evaluated through simulation and shown to improve metrics like VM utilization and task completion time over round-robin methods. The study advocates for future algorithm advances incorporating machine learning to better address dynamic load balancing challenges in cloud computing environments.
This document describes a multi-path routing algorithm for IP networks based on flow optimization. It presents an intra-domain routing algorithm that uses multi-commodity flow optimization to enable load-sensitive forwarding over multiple paths without being constrained by traditional routing protocols like OSPF. The key idea is to aggregate all traffic destined for the same egress node into one commodity during optimization, reducing the number of commodities significantly. This makes the computation tractable and allows forwarding based on destination addresses.
Analysis of Impact of Graph Theory in Computer ApplicationIRJET Journal
This document discusses several applications of graph theory in computer science. It summarizes how graph theory is used in map coloring, mobile phone networks, computer network security, modeling ad-hoc networks, fault tolerant computing systems, and clustering web documents. Graph theory provides structural models that can represent problems in these domains and enable new algorithms and solutions. Key applications mentioned include using graph coloring for frequency assignment in mobile networks, modeling network topology for worm propagation analysis, and representing documents and their relationships as graphs for clustering. Overall, the document outlines how graph theoretical concepts and methodologies are widely utilized to solve problems in computer science research areas.
CONFIGURABLE TASK MAPPING FOR MULTIPLE OBJECTIVES IN MACRO-PROGRAMMING OF WIR...ijassn
Macro-programming is the new generation advanced method of using Wireless Sensor Network (WSNs), where application developers can extract data from sensor nodes through a high level abstraction of the system. Instead of developing the entire application, task graph representation of the WSN model presents simplified approach of data collection. However, mapping of tasks onto sensor nodes highlights several problems in energy consumption and routing delay. In this paper, we present an efficient hybrid approach of task mapping for WSN – Hybrid Genetic Algorithm, considering multiple objectives of optimization – energy consumption, routing delay and soft real time requirement. We also present a method to configure the algorithm as per user's need by changing the heuristics used for optimization. The trade-off analysis between energy consumption and delivery delay was performed and simulation results are presented. The algorithm is applicable during macro-programming enabling developers to choose a better mapping according to their application requirements.
CONFIGURABLE TASK MAPPING FOR MULTIPLE OBJECTIVES IN MACRO-PROGRAMMING OF WIR...ijassn
Macro-programming is the new generation advanced method of using Wireless Sensor Network (WSNs),
where application developers can extract data from sensor nodes through a high level abstraction of the
system. Instead of developing the entire application, task graph representation of the WSN model presents
simplified approach of data collection.
Identification of Geometric Shapes with RealTime Neural NetworksEswar Publications
This article presents the implementation of an identification system of geometric figures and their respective colors, this made with neural networks by using Backpropagation control implementation. This paper describes the process of extracting characteristic patterns of images, with the help of Artificial Neural Networks. The information Neuronal Network along with additional data of images and colors, will be stored in a database which will be put dynamic that will evolve with the figures they will be learning this by implementing a PID created in MATLAB Software. Subsequent to perform image capture with an independent PC WEBCAM. This processes the image and along with the data acquired and processed by the neural network in the pattern of shapes and colors. For image processing libraries MATLAB be used both in the implementation of a system acquisition by WEBCAM.
Hybrid Task Scheduling Approach using Gravitational and ACO Search AlgorithmIRJET Journal
The document proposes a hybrid task scheduling approach for cloud computing called ACGSA that combines ant colony optimization and gravitational search algorithms. It describes using the Cloudsim simulator to test the performance of ACGSA and comparing it to ant colony optimization. The results show that ACGSA achieves better performance than the basic ant colony approach on relevant parameters like task scheduling time and resource utilization.
Machine learning in Dynamic Adaptive Streaming over HTTP (DASH)Eswar Publications
Recently machine learning has been introduced into the area of adaptive video streaming. This paper explores a novel taxonomy that includes six state of the art techniques of machine learning that have been applied to Dynamic Adaptive Streaming over HTTP (DASH): (1) Q-learning, (2) Reinforcement learning, (3) Regression, (4) Classification, (5) Decision Tree learning, and (6) Neural networks.
11 Construction productivity and cost estimation using artificial BenitoSumpter862
This chapter discusses using artificial neural networks (ANNs) to estimate construction project productivity and costs. ANNs can learn from previous examples to predict outputs like cost and schedule based on input factors. The chapter provides an overview of ANNs and examples of their use in construction cost and duration estimation. It then presents a framework for developing ANNs for productivity and cost predictions, and provides a detailed case study applying ANNs to estimate productivity of precast installation activities. The case study ANN was able to predict installation times with an average error of around 20%, demonstrating the potential of ANNs for aiding construction cost and schedule estimates.
11 Construction productivity and cost estimation using artificial AnastaciaShadelb
11 Construction productivity and cost estimation using artificial neural networks
Introduction
Because of the uncertainties and complexities involved in construction projects, expert system applications and artificial intelligence are helpful in the context of construction engineering and management. This chapter focuses on the applications of artificial neural networks (ANNs) for productivity and cost estimations, which are among the most crucial tasks of construction managers and general estimators.
The main objective of this chapter is to provide practical explanations of how to design, develop, analyse and validate ANNs as robust and reliable tools for productivity and cost estimations. An introduction to ANNs is provided, and several examples from the literature that have used ANNs in different areas of construction productivity and cost predictions are listed. As a result, a framework is presented to serve as a general guide on how to develop ANNs, and based on that, a detailed example is discussed to show the application in a real construction project setting. By the end of the chapter, readers should have some basic background about ANNs and should be able to develop a simple but efficient ANN for their own construction projects.
Artificial neural networks (ANNs)
An artificial neural network (ANN) can be defined as a massive parallel distributed processor composed of simple processing units (neurons) which are capable of storing experiential knowledge and retrieving it for future use (Haykin 1999). Neurons communicate by sending signals to each other over a large number of weighted connections. Thus, ANNs can be considered as an information processing technology that, by learning from different experiences and generalizing from previous examples, can simulate the human brain system. A simple schematic diagram of a neuron is shown in Figure 11.1.
Figure 11.1 shows that each neuron has two distinct segments: a summing junction that sums up the received inputs from neighbours and an activation function that computes the output signal, which is propagated to other neurons. The activation function can be theoretically in any form such as signum, linear or semilinear, hyperbolic tangent and sigmoid functions.
Figure 11.1 Schematic diagram of a neuron
To form a network, neurons are grouped into several layers, namely input, hidden and output layers. Two types of network topologies are shown in Figure 11.2:
· Feed-forward networks: data flows strictly from input to output layers, and no feedback connections are allowed.
· Recurrent networks: feedback connections are allowed to provide data flow from the following layers to the preceding layers.
Figure 11.2 Different topologies of ANNs (Alavala 2006)
An ANN should be arranged in such a way that it can provide the desired outputs for a set of inputs presented to the network. To do so, either connection weights should be set using prior knowledge or the network should be trained by training sa ...
11 construction productivity and cost estimation using artificial Vivan17
This chapter discusses using artificial neural networks (ANNs) to estimate construction project productivity and costs. ANNs can learn from previous examples to predict outputs like cost and schedule based on input data. The chapter provides an overview of ANNs and examples of their use in construction cost and duration estimation. It then presents a framework for developing ANNs for productivity and cost predictions, and provides a detailed case study applying ANNs to estimate productivity of precast installation activities. The case study ANN was able to predict installation times with an average error of around 20%, demonstrating the potential of ANNs for aiding construction cost and schedule estimates.
A Review - Synchronization Approaches to Digital systemsIJERA Editor
Synchronization is a prime requirement in the process of Digital systems. Wherein new devices are upcoming
towards providing higher service level, advanced distributed systems are been integrated onto a single platform
for higher service provision. However with the integration of large processing units, the distributed processing
needs a high level synchronization with minimum processing overhead. The issue of synchronization was
processed by various approaches. This paper outlines a brief review on the developments made in the field of
synchronization approach to digital system, under distributed mode operation.
Providing a multi-objective scheduling tasks by Using PSO algorithm for cost ...Editor IJCATR
This article is intended to use the multi-PSO algorithm for scheduling tasks for cost management in cloud computing. This means that
any migration costs due to supply failure consider as a one objective and each task is a little particle and recognize by use of the
appropriate fitness schedule function (how the particles arrangement) that cost at least amount of total expense. In addition to, the weight
is granted to the each expenditure that reflects the importance of cost. The data which is used to simulate proposed method are series of
academic and research data that are prepared from the Internet and MATLAB software is used for simulation. We simulate two issues,
in the first issue, consider four task by four vehicles and divide tasks. In the second issue, make the issue more complicated and consider
six tasks by four vehicles. We write PSO's output for each two issues of various iterations. Finally, the particles dispersion and as well
as the output of the cost function were computed for each pa
RSDC (Reliable Scheduling Distributed in Cloud Computing)IJCSEA Journal
This document summarizes the PPDD algorithm for scheduling divisible loads originating from multiple sites in distributed computing environments. The PPDD algorithm is a two-phase approach that first derives a near-optimal load distribution and then considers actual communication delays when transferring load fractions. It guarantees a near-optimal solution and improved performance over previous algorithms like RSA by avoiding unnecessary load transfers between processors.
Capella Based System Engineering Modelling and Multi-Objective Optimization o...MehdiJahromi
This document proposes using the Capella modeling tool and ARCADIA framework to model and optimize a distributed avionics system. Specifically, it will develop a simplified model of a Distributed Integrated Modular Avionics (DIMA) system in Capella, extract parameters to specify an optimization problem, and evaluate different cost functions to optimize tasks allocation and hardware placement for the DIMA architecture. The goal is to demonstrate how model-based systems engineering tools can help automate and improve the design of complex avionics systems.
A weighted-sum-technique-for-the-joint-optimization-of-performance-and-power-...Cemal Ardil
The document presents a self-adaptive weighted sum technique for jointly optimizing performance and power consumption in data centers. It formulates the problem as a multi-objective optimization to minimize total power consumption and task completion time. The proposed technique adapts weights during optimization to better explore non-convex regions of the solution space, unlike traditional weighted sum methods. It was tested on data from a satellite control network and showed improved results over greedy heuristics and competitive performance against optimal solutions for smaller problems.
Multi-objective tasks scheduling using bee colony algorithm in cloud computingIJECEIAES
This document presents a new approach for scheduling multi-objective tasks in cloud computing using an artificial bee colony algorithm. The proposed algorithm aims to optimize response time, schedule length ratio, and efficiency. It models tasks as bees that are assigned to processing elements in data centers to minimize completion time while balancing resource loads. The results showed the bee colony algorithm achieved better performance than other scheduling methods in cloud computing environments.
Comparative Study of Neural Networks Algorithms for Cloud Computing CPU Sched...IJECEIAES
Cloud Computing is the most powerful computing model of our time. While the major IT providers and consumers are competing to exploit the benefits of this computing model in order to thrive their profits, most of the cloud computing platforms are still built on operating systems that uses basic CPU (Core Processing Unit) scheduling algorithms that lacks the intelligence needed for such innovative computing model. Correspdondingly, this paper presents the benefits of applying Artificial Neural Networks algorithms in regards to enhancing CPU scheduling for Cloud Computing model. Furthermore, a set of characteristics and theoretical metrics are proposed for the sake of comparing the different Artificial Neural Networks algorithms and finding the most accurate algorithm for Cloud Computing CPU Scheduling.
Time and Reliability Optimization Bat Algorithm for Scheduling Workflow in CloudIRJET Journal
This document describes using a meta-heuristic optimization algorithm called the Bat Algorithm (BA) to schedule workflows in cloud computing environments. The BA is applied to optimize a multi-objective function that minimizes workflow execution time and maximizes reliability while keeping costs within a user-specified budget. The BA is compared to a basic randomized evolutionary algorithm (BREA) that uses greedy approaches. Experimental results show the BA performs better by finding schedules that have lower execution times and higher reliability within the given budget constraints. The BA is well-suited for this problem because it can efficiently search large solution spaces and automatically focus on optimal regions like other metaheuristics.
Effective and Efficient Job Scheduling in Grid ComputingAditya Kokadwar
The integration of remote and diverse resources and the increasing computational needs of Grand Challenges problems combined with the faster growth of the internet and communication technologies leads to the development of global computational grids. Grid computing is a prevailing technology, which unites underutilized resources in order to support sharing of resources and services distributed across numerous administrative region. An efficient and effective scheduling system is essentially required in order to achieve the promising capacity of grids. The main goal of scheduling is to maximize the resource utilization and minimize processing time and cost of the jobs. In this research, the objective is to prioritize the jobs based on execution cost and then allocate the resources with minimum cost by merging it with conventional job grouping strategy to provide the solution for better and more efficient job scheduling which is beneficial to both user and resource broker. The proposed scheduling approach in grid computing employs a dynamic cost-based job scheduling algorithm for making an efficient mapping of a job to available resources in the grid. It also improves communication to computation ratio (CCR) and utilization of available resources by grouping the user jobs before resource allocation.
DYNAMIC TASK PARTITIONING MODEL IN PARALLEL COMPUTINGcscpconf
Parallel computing systems compose task partitioning strategies in a true multiprocessing
manner. Such systems share the algorithm and processing unit as computing resources which
leads to highly inter process communications capabilities. The main part of the proposed
algorithm is resource management unit which performs task partitioning and co-scheduling .In
this paper, we present a technique for integrated task partitioning and co-scheduling on the
privately owned network. We focus on real-time and non preemptive systems. A large variety of
experiments have been conducted on the proposed algorithm using synthetic and real tasks.
Goal of computation model is to provide a realistic representation of the costs of programming
The results show the benefit of the task partitioning. The main characteristics of our method are
optimal scheduling and strong link between partitioning, scheduling and communication. Some
important models for task partitioning are also discussed in the paper. We target the algorithm
for task partitioning which improve the inter process communication between the tasks and use
the recourses of the system in the efficient manner. The proposed algorithm contributes the
inter-process communication cost minimization amongst the executing processes.
Demand-driven Gaussian window optimization for executing preferred population...IJECEIAES
Scheduling is one of the essential enabling technique for Cloud computing which facilitates efficient resource utilization among the jobs scheduled for processing. However, it experiences performance overheads due to the inappropriate provisioning of resources to requesting jobs. It is very much essential that the performance of Cloud is accomplished through intelligent scheduling and allocation of resources. In this paper, we propose the application of Gaussian window where jobs of heterogeneous in nature are scheduled in the round-robin fashion on different Cloud clusters. The clusters are heterogeneous in nature having datacenters with varying sever capacity. Performance evaluation results show that the proposed algorithm has enhanced the QoS of the computing model. Allocation of Jobs to specific Clusters has improved the system throughput and has reduced the latency.
Image Result For Sample Art Reflection Paper ReflectivAlicia Edwards
The document discusses One Day in the Life of Ivan Denisovich, a novel that follows a day in the life of Ivan Denisovich Shukhov, a prisoner in a Stalinist labor camp in the Soviet Union. It shows Shukhov's struggles and hardships over the course of this single day in the camp. The day demonstrates the difficult conditions prisoners faced, including cold weather, hard labor, and lack of food. The novel provides insight into life in the Soviet labor camps through focusing intensely on one representative day for the main character.
015 How To Start An Interview Essay ExampleAlicia Edwards
This document discusses abortion laws and the case of Roe v. Wade. It defines abortion as ending a pregnancy to cause fetal death. Abortions were common in the 1800s but secret due to public scrutiny and some being illegal. Risk of infection was high without modern sterilization techniques. States modified abortion laws over time based on political agendas. Roe v. Wade was a landmark Supreme Court case that established a woman's right to choose to have an abortion without excessive government restriction.
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Macro-programming is the new generation advanced method of using Wireless Sensor Network (WSNs), where application developers can extract data from sensor nodes through a high level abstraction of the system. Instead of developing the entire application, task graph representation of the WSN model presents simplified approach of data collection. However, mapping of tasks onto sensor nodes highlights several problems in energy consumption and routing delay. In this paper, we present an efficient hybrid approach of task mapping for WSN – Hybrid Genetic Algorithm, considering multiple objectives of optimization – energy consumption, routing delay and soft real time requirement. We also present a method to configure the algorithm as per user's need by changing the heuristics used for optimization. The trade-off analysis between energy consumption and delivery delay was performed and simulation results are presented. The algorithm is applicable during macro-programming enabling developers to choose a better mapping according to their application requirements.
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Machine learning in Dynamic Adaptive Streaming over HTTP (DASH)Eswar Publications
Recently machine learning has been introduced into the area of adaptive video streaming. This paper explores a novel taxonomy that includes six state of the art techniques of machine learning that have been applied to Dynamic Adaptive Streaming over HTTP (DASH): (1) Q-learning, (2) Reinforcement learning, (3) Regression, (4) Classification, (5) Decision Tree learning, and (6) Neural networks.
11 Construction productivity and cost estimation using artificial BenitoSumpter862
This chapter discusses using artificial neural networks (ANNs) to estimate construction project productivity and costs. ANNs can learn from previous examples to predict outputs like cost and schedule based on input factors. The chapter provides an overview of ANNs and examples of their use in construction cost and duration estimation. It then presents a framework for developing ANNs for productivity and cost predictions, and provides a detailed case study applying ANNs to estimate productivity of precast installation activities. The case study ANN was able to predict installation times with an average error of around 20%, demonstrating the potential of ANNs for aiding construction cost and schedule estimates.
11 Construction productivity and cost estimation using artificial AnastaciaShadelb
11 Construction productivity and cost estimation using artificial neural networks
Introduction
Because of the uncertainties and complexities involved in construction projects, expert system applications and artificial intelligence are helpful in the context of construction engineering and management. This chapter focuses on the applications of artificial neural networks (ANNs) for productivity and cost estimations, which are among the most crucial tasks of construction managers and general estimators.
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Artificial neural networks (ANNs)
An artificial neural network (ANN) can be defined as a massive parallel distributed processor composed of simple processing units (neurons) which are capable of storing experiential knowledge and retrieving it for future use (Haykin 1999). Neurons communicate by sending signals to each other over a large number of weighted connections. Thus, ANNs can be considered as an information processing technology that, by learning from different experiences and generalizing from previous examples, can simulate the human brain system. A simple schematic diagram of a neuron is shown in Figure 11.1.
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Figure 11.1 Schematic diagram of a neuron
To form a network, neurons are grouped into several layers, namely input, hidden and output layers. Two types of network topologies are shown in Figure 11.2:
· Feed-forward networks: data flows strictly from input to output layers, and no feedback connections are allowed.
· Recurrent networks: feedback connections are allowed to provide data flow from the following layers to the preceding layers.
Figure 11.2 Different topologies of ANNs (Alavala 2006)
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11 construction productivity and cost estimation using artificial Vivan17
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Analytic Hierarchy Process And Multilayer Network-Based Method For Assembly Line Balancing
1. applied
sciences
Article
Analytic Hierarchy Process and Multilayer
Network-Based Method for Assembly Line Balancing
László Nagy, Tamás Ruppert and János Abonyi *
MTA-PE “Lendület” Complex Systems Monitoring Research Group, University of Pannonia, P.O. Box 158,
H-8200 Veszprém, Hungary; laszlo.nagy@fmt.uni-pannon.hu (L.N.); ruppert@abonyilab.com (T.R.)
* Correspondence: janos@abonyilab.com
Received: 30 April 2020; Accepted: 2 June 2020; Published: 5 June 2020
Abstract: Assembly line balancing improves the efficiency of production systems by the optimal
assignment of tasks to operators. The optimisation of this assignment requires models that provide
information about the activity times, constraints and costs of the assignments. A multilayer
network-based representation of the assembly line-balancing problem is proposed, in which the
layers of the network represent the skills of the operators, the tools required for their activities
and the precedence constraints of their activities. The activity–operator network layer is designed
by a multi-objective optimisation algorithm in which the training and equipment costs as well
as the precedence of the activities are also taken into account. As these costs are difficult to
evaluate, the analytic hierarchy process (AHP) technique is used to quantify the importance of
the criteria. The optimisation problem is solved by a multi-level simulated annealing algorithm (SA)
that efficiently handles the precedence constraints. The efficiency of the method is demonstrated by a
case study from wire harness manufacturing.
Keywords: assembly-line balancing; multi-objective optimization; simulated annealing;
multilayer network
1. Introduction
Production line-based assembly lines are still the most widely applied manufacturing systems [1].
Assembly-Line Balancing (ALB) [2] deals with the balanced assignment of tasks to the workstations,
resulting in the optimisation of a given objective function without violating precedence constraints [3].
The efficiency of these optimisation tasks is mostly determined by the model of the manufacturing
process represented [4].
The concept of Industry 4.0 has already had a significant influence on how production and
assembly lines are designed [5] and managed [6]. The requirement of practical design at a high
automation level ensures that sensors and equipment can be integrated in a fast, secure, and reliable
way. In our research, we study how the interoperability capabilities of Industry 4.0 solutions can be
improved and how the efficiency of solution development can be increased.
As Internet of Things-based products and processes are rapidly developing in the industry,
there is a need for solutions that can support their fast and cost-effective implementation. There is
a need for further standardization to achieve more flexible connectivity, interoperability, and fast
application-oriented development; furthermore, advanced model-based control and optimisation
functions require a better understanding of sensory and process data [7].
Usually, production systems include multiple subsystems and layers of connectivity. Thus,
although research-based solutions for classical operations typically use a graph-based representation
of problems and flow-based optimisation algorithms, conventional single-layer networks quickly
become incapable of representing the complexity and connectivity of all the details of the production
Appl. Sci. 2020, 10, 3932; doi:10.3390/app10113932 www.mdpi.com/journal/applsci
2. Appl. Sci. 2020, 10, 3932 2 of 16
line. With the overlapping data in Industry 4.0 solutions, it should be highlighted that multilayer
networks are expected to be the most suitable options for representing modern production lines.
The concept of a multilayer network was developed to represent multiple types of relationships [8],
and these models have been proven to be applicable to the representation of complex connected
systems [9]. Network-based models can also represent how products, resources and operators are
connected [10], which is beneficial in terms of solving manufacturing cell formation problems [11].
This work demonstrates how the multilayer network representation of production lines can be utilised
in line balancing.
In the proposed novel network model, the layers represent the skills of the operators, the tools
required for the activities, and the precedence constraints of the activities. At the same time,
a multi-objective optimisation algorithm designs the assignment of activities and operators to
network layers. The proposed multilayer network approach supports the intuitive formulation
of multi-objective line balancing optimisation tasks. Besides the utilisation of operators, the utilisation
of the tools and the number of skills of an operator are also taken into account. The main advantage of
the proposed network-based representation is that the latter two objectives are directly related to the
structural properties of the optimised network.
Line balancing is a non-deterministic polynomial-time hard (NP-hard) optimisation problem,
which means that the computational complexity of the optimisation problem increases exponentially
as the dimensions of the problem increase. This challenge explains why numerous meta heuristic
approaches such as simulated annealing (SA) [12,13], hybrid heuristic optimisation [13,14],
chance-constrained integer programming [15], recursive and dynamic programming [16], as well
as tabu search [17] have been utilised in the field of production management. Fuzzy set theory
provides a transparent and interpretable framework to represent the uncertainty of information and
solve the ALB problem [18,19]. Among the wide range of heuristic methods capable of achieving
reasonable solutions [20], SA is the most widely used search algorithm [21], so it has already been
applied to solve mixed and multi-model line-balancing problems [22].
To deal with the complexity of this problem, an SA algorithm was also developed. The proposed
algorithm utilises a unique problem-oriented sequential representation of the assignment problem
and applies a neighbourhood-search strategy that generates feasible task sequences for every iteration.
Since the algorithm has to handle multiple aspects of line balancing, the analytic hierarchy process
(AHP) technique is used to quantify the importance of the objectives, also known as Saaty’s method [23].
AHP is a method for multi-criteria decision-making which is used to evaluate complex multiple criteria
alternatives involving subjective judgments [24]. This method is a useful and practical approach to
solving complex and unstructured decision-making problems by calculating the relative importance
of the criteria based on the pairwise comparison of different alternatives [25]. The method has been
widely applied thanks to its effectiveness and interpretability. Two papers were found in which it
has already been applied to determine the cost function of multi-objective SA optimisation problems.
In the first case study of supplier selection, AHP was applied to calculate the weight of every objective
by applying the Taguchi method [26] (Adaptive Tabu Search Algorithm—ATSA [27]). In contrast,
in the second report, this concept was applied to the maintenance of road infrastructure [28].
The novelties of the work are the following:
• In Section 2, the main problem formulation is introduced, including the multilayer network
representation of multiple aspects concerning the balancing of production lines, and the details of
the objective function.
• In Section 3, an SA algorithm will be introduced based on a novel sequential representation
of the line-balancing problem and the search algorithm that guarantees the fulfilment of the
precedence constraints.
• Section 4 demonstrates how AHP can be used to aggregate the multi layer network-represented
objectives of the line-balancing problem for SA.
3. Appl. Sci. 2020, 10, 3932 3 of 16
2. Problem Formulation
In this section, the problem formulation is presented. First, the representation of production line
modelling with the multilayer network is introduced in Section 2.1. The details of the minimised
function and its AHP-based aggregation are given in Section 2.2.
2.1. Multilayer Network-Based Representation of Production Lines
The proposed network model of the production line consists of a set of bipartite graphs
that represent connections between operators, o = {o1, . . . , oNo }; skills of the operators needed
to perform the given activity, s = {s1, . . . , sNs }; equipment, e = {e1, . . . , eNe }; activities
(operations), a = {a1, . . . , aNa }; and the precedence constraints between activities, a
′
=
n
a1
′
, . . . , a
′
Na
o
.
The relationships between these sets are defined by bipartite graphs Gi,j = (Oi, Oj, Ei,j) represented by
A[Oi, Oj] biadjacency matrices, where Oi and Oj denote a general representation of the sets of objects,
such that Oi, Oj ∈
n
s, e, a
′
, a, o
o
.
The edges of these bipartite networks represent structural relationships; e.g., the biadjacency
matrix A[a, a′] represents the precedence constraints or A[a, o] represents the assignments of
activities to operators. Moreover, the edge weights can be proportional to the number of shared
components/resources or time/cost (see Table 1) [10].
Table 1. Definition of the biadjacency matrices of the bipartite networks used to illustrate how a
multidimensional network can represent a production line.
Nodes Description
W Activity (a)–operator (o) Operator assigned to the activity
S Activity (a)–skill (s) Skill/education required for a category of activities
E Activity (a)–equipment (e) Equipment which is in use in an activity
A′ Activity (a)–activity (a′) Precedence constraint between activities
As can be seen in Figure 1, these bipartite networks are strongly connected. The proposed model
can be considered as an interacting or interconnected network [8], where bipartite networks define
the layers. Since different types of connections are defined, the model can also be handled as a
multidimensional network. As illustrated in Figure 2, when relationships between the sets Oi and Oj
are not directly defined, it is possible to evaluate the relationship between their elements oi,k and oj,l in
terms of the number of possible paths or the length of the shortest path between these nodes [10].
Figure 1. Illustrative network representation of a production line. The definitions of the symbols are
given in Table 1.
4. Appl. Sci. 2020, 10, 3932 4 of 16
Figure 2. Projection of a property connection.
In the case of connected unweighted multipartite graphs, the number of paths intersecting the set
O0 can be easily calculated based on the connected pairs of bipartite graphs as follows:
AO0
[Oi, Oj] = A[O0, Oi]T
× A[O0, Oj] . (1)
In the proposed network model, the optimisation problem is defined by the allocation of tasks that
require the allocation of different skills and tools to an operator that might necessitate extra training,
labour and investment costs. The main benefit of the proposed network representation is that these
costs can be directly evaluated based on the products of the biadjacency matrices S and W:
A[s, o] = A[s, a]A[a, o] = SW. (2)
The resultant network A[s, o] represents how many times a given skill should be utilised by an
operator, while its unweighted version Au[s, o] models which skills the operators should have.
The design of the presented network model is based on the analysis of the semantically
standardized models of production lines [29], and the experience gained in the development project
connected to the proposed case study. The details of the multilayer network-based modelling of a
wire-harness production process can be found in [10].
2.2. The Objective Function
A simple assembly line balancing problem (SALBP) assigns Na tasks/activities to No
workstations/operators. Each activity is assigned to precisely one operator, and the sum of task
times of workstation should be less or equal to the cycle time Tc [30]. Precedence relations between
activities must not be violated [31]. There are two important variants of this problem [32]: SALBP-1
aims to minimise No for a given Tc, while the goal of SALBP-2 is to minimise Tc for a predefined
No [1,33,34]. In this paper, the SALBP-2 problem was investigated and extended to include the
following skill and equipment-related objective functions:
Station-time-related objective: The main objective of line balancing is to minimise the cycle time
Tc, which is equal to the sum of the maximum of the station times Tj. The utilisation of the whole
assembly line can be calculated as follows:
Tc = arg max
j
Tj =
Na
∑
i=1
wi,jti, (3)
where ti represents the elementary activity times of the ai-th activity.
As the theoretical minimum of Tc is
T∗
c =
∑
Na
i=1 ti
No.
, (4)
the following ratio evaluates the efficiency of the balancing of the activity times:
5. Appl. Sci. 2020, 10, 3932 5 of 16
QT(π) =
T∗
c
Tc
=
∑
Na
i=1 ti
No
∑
Na
i=1 wi,jti.
(5)
Skill-related (training) objective: The training cost is calculated with the node degree between
skill-operator elements s − o. The number of skills Ns is divided by the sum of the node degrees ki
between sub-networks s and o in the multilayer representation:
QS(π) =
Ns
∑
s−o,o
i ki.
(6)
Equipment-related objective function: The equipment cost is calculated with the node degree
between equipment-operator elements e − o. The number of pieces of equipment Ne is divided by the
sum of the node degrees ki between sub-networks e and o in the multilayer representation:
QE(π) =
Ne
∑
e−o,o
i ki.
(7)
Since the importance of these objectives is difficult to quantify, a pairwise comparison is used to
evaluate their relative importance, and the analytic hierarchy process (AHP) is used to determine the
weights λ in the objective function:
Q(π) = λ1QT(π) + λ2QS(π) + λ3QE(π), (8)
where QT(π) ∈ [0, 1] represents the balance of the production line, and QS(π) ∈ [0, 1] and QE(π) ∈
[0, 1] measure the efficiency of how the skills and tools are utilised, respectively.
The application of AHP-based weighting is beneficial to integrate the normalised values of the
easy to evaluate station-time and equipment-related objectives, and the less specific training-related
costs. Although the pairwise comparison of the importance of these objectives and cost-items is
subjective, the consistency of the comparisons can be evaluated based on the numerical analysis of the
resulted comparison matrices (which will be shown in the next section), which clarifies the reason for
our choice of AHP as an ideal tool to extract expert knowledge for the formalisation of the cost function.
3. Simulated Annealing-Based Line-Balancing Optimization
This section presents the proposed optimisation algorithm. The representation of the SA problem
is introduced in Section 3.1. Section 3.2 discusses how the precedence constraints of the activities are
represented, while Section 3.3 presents how the assignment of activities to operators is formulated by
a sequencing problem that can be efficiently solved by the proposed simulated annealing algorithm.
3.1. Representation of the Problem
In the proposed network representation (Figure 1), the assignment of activities to operators is
defined by the elements wi,j of the matrix W that represent the ith activity assigned to the jth operator.
Instead of the direct optimisation of these Na × No elements, a sequence Nπ = Na + No − 1 is optimised,
where Na represents the number of activities and No denotes the number of operators.
The concept of sequence-based allocation is illustrated in Figure 3, where the horizontal axis
represents the fixed order of the operators oj and the vertical axis stands for the activities ai , where π(i)
represents the index of the activity by the ith sequence number. The ordered activities are assigned
to the operators by No − 1 boundary elements, represented as aπ(i) = ∗, which ensure that the next
activity in the sequence is assigned to the following operator.
6. Appl. Sci. 2020, 10, 3932 6 of 16
Figure 3. Illustration of the sequencing method. The activities are separated into the different groups
of activities that are assigned to different operators.
3.2. Handling Precedence Constraints
In addition to these three objectives of the simulated production line, a so-called soft limit is also
defined, which is the amount of the unaccomplished precedence of the activities (A′). This limitation
of the order with regard to the activities is stored in the multilayer network.
The completion of a task is a precondition for the start of another because tasks depend on other
tasks. The π sequence has some constraining condition and cannot be entirely arbitrary. The precedence
graph is used to represent these dependencies in SALBP [1,35,36]. Figure 4 shows a problem from
a well-known example by Jackson [37] with Na = 11 tasks, where task 7 requires tasks 3–5 to be
completed directly (direct predecessor) and task 1 indirectly (indirect predecessor). The precedence
graph can be described by matrix A′(i, j), i, j = 1, 2, . . . , Na, where A′(i, j) = 1 if task i is the direct
predecessor of task j, otherwise, it is 0 [32]. The precedence graph is partially ordered if tasks cannot be
performed in parallel. It must be determined whether a permutation π = (π1, π2, . . . , πNa ) is feasible
or not according to the precedence constraint.
Based on the transitive closure A∗ of A′, π is feasible if A∗(pj, pi) = 0, ∀i, j, i j; otherwise, π is
infeasible [32]. A sub-sequence (πi, πi+1, . . . , πj), where i j of π, can be defined by π(i:j). For example,
a feasible sequence π of the precedence graph in Figure 4 is π = (1, 4, 3, 2, 5, 7, 6, 8, 9, 10, 11) and
π(2:4) = (4, 3, 2) is a sub-sequence of π.
Figure 4. Precedence graph of the example problem taken from Jackson [32,37].
As will be presented in the next subsection, the key idea of the algorithm is that it determines the
interchangeable sets of activity pairs and uses these in the guided simulated annealing optimisation.
7. Appl. Sci. 2020, 10, 3932 7 of 16
3.3. Sequence-Based Activity Grouping and Operator Assignment
The optimization algorithm is shown in Algorithm 1 and consists of the following steps:
• Generating the initial feasible sequence.
• SA I: Optimization of the sequences of the activities.
– SA II (embedded in SA I): in the case of a specific sequence, the activities are assigned to the
operators by optimizing the location of the boundary elements in sequence π as has been
presented in Figure 3, so SA I uses a cost function that relates to the optimal assignment.
Algorithm 1: Pseudocode of the proposed SA-ALB algorithm
Input: s, e, Time, Precedence
Output: π, Q(π)
Annealing: maxiter, T, Tmax, Tmin, mmax, mmin
1 α = ( Tmin
Tmax
)1/maxiter, T1 = Tmax
2 αm = ( mmin
mmax
)1/maxiter, m1 = mmax
3 Begin
4 T = Tmax; Tmax = maximum value of temperature
5 while T Tmin; Tmin = minimum value of temperature
6
7 Generate initial sequence π, which satisfies the constraints
8 Generate initial placement of the boundary elements
9 Evaluate the cost function Q(π), as functions (5), (6) and (7)
10 for i = 1 to maxiter do
11
12 Select randomly one interchangeable activity pair
13 Interchange the activities and evaluate the new solution by implementing SA II that
optimizes the placement of the boundary elements in this sequence
14 // SA II is working with the same principle as this main SA I
15
16 NewQ(πnew) = Q(πnew)
17 ∆ = Q(πnew) − Q(π)
18 if ∆ 0 then
19 π = πnew
20 Q(π) = Q(πnew)
21 else
22 if random() exp(−∆
Ti ) then
23 π = πnew
24 Q(π) = Q(πnew)
25 Ti+1 = αTi, mi+1 = αimi
26 End
4. Case Study
This study was inspired by an industrial case study of wire harness manufacturing,
where operators work with several tools that perform different activities at workstations to manufacture
cables. The problem assumes that it is possible to improve the manufacturing efficiency if the resources,
activities, skills and precedence are better designed.
The development of the proposed line-balancing algorithm is motivated by a development project
which was defined to improve the efficiency of an industrial wire harness manufacturing process [38].
8. Appl. Sci. 2020, 10, 3932 8 of 16
In this work, a subset of this model is used which consists of 24 activities, five operators, six skills and
eight pieces of equipment.
The elementary activity times that influence the line balance were determined based on expert
knowledge [39] (see Table 2).
A more detailed description of the activities, pieces of equipment and skills can be found in
Tables 2–6.
Table 2. List of the elementary activities that should be allocated in the line balancing problem.
Activity ID Description Time
A1 Connector handling 4 s
A2 Connector handling 3 s
A3 Connector handling 2 s
A4 Connector handling 3 s
A5 Insert 1st end + routing 10 s
A6 Insert 2nd end 5 s
A7 Insert 1st end + routing 10 s
A8 Insert 2nd end 5 s
A9 Insert 1st end + routing 10 s
A10 Insert 2nd end 5 s
A11 Insert 1st end + routing 10 s
A12 Insert 2nd end 5 s
A13 Insert 1st end + routing 10 s
A14 Insert 2nd end 5 s
A15 Insert 1st end + routing 10 s
A16 Insert 2nd end 5 s
A17 Insert 1st end + routing 10 s
A18 Insert 2nd end 5 s
A19 Taping 15 s
A20 Taping 13 s
A21 Taping 11 s
A22 Taping 17 s
A23 Taping 15 s
A24 Quality check 10 s
The following tables give a more detailed description of the activities, equipment (Table 3) and
skills (Table 4) which are involved in the proposed case study. Furthermore, the activity–equipment
(Table 5) and activity–skill (Table 6) connectivity matrices show the requirements of the given
base activity.
Table 3. List of equipment that should be allocated in the line balancing problem.
Equipment ID Description
E1 Connector fixture
E2 Connector fixture
E3 Routing tool
E4 Insertion tool
E5 Taping tool (expert)
E6 Taping tool (normal)
E7 Taping tool (normal)
E8 Repair tool
9. Appl. Sci. 2020, 10, 3932 9 of 16
Table 4. Description of skills that should be used in the studied production process.
Skill ID Description
S1 Connector handling skill
S2 Insertion (normal) and routing skills
S3 Insertion (expert) skill
S4 Taping (normal) skill
S5 Taping (expert) skill
S6 Quality (expert) skill
Table 5. Activity–equipment matrix that defines which equipment are required to perform a given activity.
E1 E2 E3 E4 E5 E6 E7 E8
A1 1 1
A2 1 1
A3 1 1
A4 1 1
A5 1
A6 1
A7 1
A8 1
A9 1
A10 1
A11 1
A12 1
A13 1
A14 1
A15 1
A16 1
A17 1
A18 1
A19 1
A20 1
A21 1 1
A22 1 1
A23 1 1
A24 1
Table 6. Activity–skill matrix that defines which skills are required to perform a given activity.
S1 S2 S3 S4 S5 S6
A1 1
A2 1
A3 1
A4 1
A5 1
A6 1
A8 1
A9 1
A10 1
A11 1
A12 1
A13 1
A14 1
A15 1
10. Appl. Sci. 2020, 10, 3932 10 of 16
Table 6. Cont.
S1 S2 S3 S4 S5 S6
A7 1
A16 1
A17 1
A18 1
A19 1
A20 1
A21 1
A22 1
A23 1
A24 1
The tables illustrate that the practical implementation of line balancing problems is also influenced
by how much equipment is needed for the designed production line and how many skills should be
learnt by the operators.
All the collected information is transformed into network layers, as shown in Figure 5. The top of
the figure shows the bipartite networks that represent the details of the assignments, while the bottom
of the figure represents the tree layers of the network that define the activity–operator, skill–operator,
and equipment–operator assignments. As can be seen, this representation is beneficial as it shows how
similar operators, skills and equipment can be grouped into clusters.
Figure 5. Illustration of the skill–operator and equipment–operator assignments after line balancing.
11. Appl. Sci. 2020, 10, 3932 11 of 16
Although this is not shown in the figure, the weights of the edges represent the costs or benefits
of the assignments. The final form of the network is formed based on a multi-objective optimisation of
the sets of active edges.
As some of these objectives are difficult to measure, we utilised the proposed AHP-based method
to convert the pairwise comparisons of the experts into weights of criteria. The structure of the decision
problem is represented in Figure 6. As this figure illustrates, the AHP is used to compare difficult to
evaluate equipment and skill assignment costs and the importance of the objectives. The pairwise
comparison was performed by a process engineer, and the resulting comparison matrices can be found
in Tables 7–9. Based on the analysis of the the eigenvalues of these matrices [25], we found that the
evaluations were consistent.
Since the activities cannot be performed in parallel, a precedence graph defines the most crucial
question, namely whether a permutation of sequence π is feasible. Based on the transitive closure of
the adjacency matrix of the graph, the interchangeable sets of activities can be defined as depicted
in Figure 7.
The result of the optimization is shown in Figure 5, which illustrates that the five operators
assigned to different skills and pieces of equipment.
The reliability and the robustness of the proposed method are evaluated by ten independent runs
of the optimisation algorithm to highlight how the stochastic nature of the proposed method influences
the result, as well as showing the effect of the number of operators on the solutions. The aim of the
analysis of the independent runs was to estimate the variance of the solutions caused by the stochastic
nature of the process and the optimisation algorithm. The sample size of such repeat studies can be
determined based on the statistical tests of the estimated variance. In our analysis, we found that ten
experiments were sufficient to get a proper estimation of the variance (which is in line with the widely
applied ten-fold cross-validation concept).
Figure 6. Analytic hierarchy process (AHP) used to solve a decision problem.
Table 7. AHP TOP matrix that shows the relative importance of the objectives. It can be seen that,
in this pair-wise comparison, the skill-related cost is evaluated as being twice as important as the
equipment-related costs.
Balancing Equipment Skill
Balancing 2.00 4.00
Equipment 0.50 2.00
Skill 0.25 0.50
12. Appl. Sci. 2020, 10, 3932 12 of 16
Table 8. AHP equipment matrix that shows the relative importance of the equipment.
E1 E2 E3 E4 E5 E6 E7 E8
E1 1 0.33 0.50 2 3 3 2
E2 1 0.33 0.50 2 3 3 2
E3 3 3 2 5 7 7 5
E4 2 2 0.50 3 5 5 3
E5 0.50 0.50 0.20 0.33 2 2 1
E6 0.33 0.33 0.14 0.20 0.50 1 0.50
E7 0.33 0.33 0.14 0.20 0.50 1 0.50
E8 0.50 0.50 0.20 0.33 1 2 2
Table 9. AHP skill matrix that shows the relative importance of the skills.
S1 S2 S3 S4 S5 S6
S1 0.20 0.30 0.50 0.50 0.14
S2 5 2 3 3 0.50
S3 3 0.50 2 2 0.33
S4 2 0.30 0.50 1 0.20
S5 2 0.30 0.50 1 0.20
S6 7 2 3 5 5
Figure 7. Possible path (left), precedence (middle) and transitive closure (right) of the activities (the
unmarked pairs are interchangeable).
Figure 8 presents the different time, skill and equipment-related objectives in the case of different
operators. As the results show, the increase in the number of operators decreases the efficiency of
the utilisation of the tools and skills (this trend is the main driving force for forming manufacturing
cells). The process can be well balanced in the case of 3–5 operators; e.g., in the case of five operators,
in one of the best solutions, the balancing objectives are a time cost of 94.3%, training cost of 75.0%
and equipment cost of 72.8%. Figure 9 shows the different total activity times of each operator during
the simulation. In this case, the station times do not differ greatly, and the result is optimal [10].
The proposed algorithm was implemented in MATLAB and is available on the website of the authors
(www.abonyilab.com/about-us/software-and-data); interested readers can make further comparisons,
and the proposed problem can serve as a benchmark for constrained multi-objective line balancing.
Based on the simple modification of the code, the algorithm can be compared to classical simulated
annealing-based line balancing; this comparison demonstrates that the main benefit of the proposed
constrained handling is the acceleration of the optimisation. At the same time, the application of the
inner-loop-based assignment significantly reduces the variance and increases the chance of obtaining
improved line balancing results.
13. Appl. Sci. 2020, 10, 3932 13 of 16
3 4 5 6
NO
0.5
0.6
0.7
0.8
0.9
1
Q
T(
)
3 4 5 6
NO
0.5
0.6
0.7
0.8
0.9
1
Q
S(
)
3 4 5 6
NO
0.5
0.6
0.7
0.8
0.9
1
Q
E(
)
Figure 8. Boxplot of time, skill and equipment-related objectives for different independent runs of the
algorithm and with different numbers of operators.
Activity time of operator
1 2 3 4 5
Operator ID
0
5
10
15
20
25
30
35
40
45
Activity
time
[s]
Figure 9. Comparison of the operators’ activity times.
5. Conclusions
We proposed an assembly line balancing algorithm to improve the efficiency of production
systems by the multiobjective assignment of tasks to operators. The optimisation of this assignment is
based on a multilayer network model that provides information about the activity times, constraints
and benefits (objectives) of the assignments, where the layers of the network represent the skills of the
operators, the tools required for their activities and the precedence constraints of their activities.
The training and equipment costs as well as the precedence of the activities are also taken into
account in the activity–operator layer of the network. As these costs and benefits are difficult to
evaluate, the analytic hierarchy process (AHP) technique is used to quantify the importance of the
criteria. The optimisation problem is solved by a multi-level simulated annealing algorithm (SA) that
efficiently handles the precedence constraints thanks to the proposed problem-specific representation.
The proposed algorithm was implemented in MATLAB and the applicability of the method
demonstrated with an industrial case study of wire harness manufacturing. The results confirm that
multilayer network-based representations of optimisation problems in manufacturing seem to be
potential promising solutions in the future.
The main contribution of the work is that it presents tools that can be used for the efficient
representation of expert knowledge that should be utilised in complex production management
14. Appl. Sci. 2020, 10, 3932 14 of 16
problems. The proposed multilayer network-based representation of the production line supports
the incorporation of advanced (ontology-based) models of production systems and provides an
interpretable and flexible representation of all the objectives of the line balancing problem.
The AHP-based pairwise comparison of the importance of the nodes, edges and complex paths of
this network can be used to evaluate the objectives of the optimisation problems. The integration of
the network-based knowledge representation and the AHP-based knowledge extraction makes the
application of the proposed methodology attractive in complex optimisation problems.
Author Contributions: L.N., T.R. and J.A. developed the methodology and software; L.N. prepared the original
draft; J.A. reviewed and edited the manuscript. All authors have read and agreed to the published version of
the manuscript.
Funding: This research was supported from the Higher Educational Institutional Excellence Program 2019
the grant of the Hungarian Ministry for Innovation and Technology (Grant Number: NKFIH-1158-6/2019).
Tamás Ruppert was supported by the project 2018-1.3.1-VKE-2018-00048–Development of intelligent Industry 4.0
solutions of production optimization in existing plants and the ÚNKP-19-3 New National Excellence Program of
the Ministry of Human Capacities.
Acknowledgments: The authors are grateful for the valuable comments and suggestions offered by the
anonymous reviewers.
Conflicts of Interest: The authors declare no conflicts of interest.
Abbreviations
The following abbreviations are used in this manuscript:
SA Simulated annealing
ALB Assembly line balancing
Gi,j Bipartite graphs between the ith and jth sets of objects
Oj, Oj General representation of a set of objects as Oi, Oj ∈
n
s, e, a
′
, a, w
o
a = a1, . . . , aNa
Index of activities
o = o1, . . . , oNo
Index of operators
s = s1, . . . , sNs
Index of skills
e = e1, . . . , eNe
Index of equipment
w = w1, . . . , wNw
Index of workstations
W Workstation assigned for the activity, Na × Nw
O Operators assigned for the activity, Na × No
S Skills assigned for the activity, Na × Ns
E Equipment assigned for the activity, Na × Ne
A′ Precedence constraint between activities, Na × Na
T = t1, . . . , tNa
Activity time
c1 Station-time-related cost
c2 Skill-related (training) cost
c3 Equipment-related cost
Tc Cycle time
Nw Number of workstations
No Number of operators
Ns Number of skills
Ne Number of pieces of equipment
Nπ Number of sequence elements
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